A gate-based model for the concatenated GKP-surface code catering to a superconducting platform was considered in Refs. [1]}, [2]}, [3]}.
In these works, each GKP qubit in the surface code first undergoes a round of GKP error correction, after which the stabilizer measurements for the surface code are performed.
The noise considered in Ref. [1]}, [2]} is a Gaussian classical noise channel applied to all GKP qubits and prior to all homodyne measurements in both the GKP error correction and the parity check measurements.
Ref. [3]} considers the same noise model but applied now to the circuit level, and explicitly includes error feedback.
An improved threshold for the surface-GKP code was obtained in Ref. [7]} by designing bias in the noise.
